$4.$ Consider the following tasks, along with their duration and required predecessors. $(30$ points$)$

ID Description Precede ID Duration

A Complete Foundation $-6$

B Connect Plumbing A $6$

C Install Drywall A $2$

D Paint Interior Walls C $4$

E Install Trim Carpentry D $3$

F Install Windows A $4$

G Paint Exterior Walls F $1$

H Complete Inspection B$,$ E$,$ G $0$

I Attain Client Approval H $2$

J Close Sale I $1$

a$.$ Draw the PERT flow, labeling ECT and LCT for each event. Please embed the drawing in this document, either in electronic format such as MS Visio or hand$-$drawn sketch.

b$.$ Determine the critical path time and available slack time.